*

A composite number

*
is a optimistic integer
*
1" /> i beg your pardon is not prime (i.e., i beg your pardon has factors other 보다 1 and also itself). The first couple of composite number (sometimes dubbed "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16, ... (OEIS A002808), who prime decompositions are summarized in the adhering to table. Note that the number 1 is a special case which is considered to be neither composite nor prime.

You are watching: What is the sum of the first four composite numbers

*
prime factorization
*
prime factorization
4
*
20
*
6
*
21
*
8
*
22
*
9
*
24
*
10
*
25
*
12
*
26
*
14
*
27
*
15
*
28
*
16
*
30
*
18
*
32
*

The

*
th composite number
*
have the right to be generated using the benidormclubdeportivo.org Language code

Composite := FixedPoint + 1&, n>The Dirichlet generating function of the characteristic duty of the composite numbers

*
is provided by

*
)/(n^s)" />
*
*

(1)
*
*
*

(2)
*
*
*

(3)

where

*
is the Riemann zeta function,
*
is the element zeta function, and also
*
" /> is an Iverson bracket.

There room an infinite variety of composite numbers.

The composite number problem asks if there exist positive integers

*
and also
*
such that
*
.

A composite number

*
can constantly be created as a product in at least two ways (since
*
is always possible). Call these 2 products


*

(4)

then it is clear the situation that

*
(
*
divides
*
). Set


*

(5)

where

*
is the component of
*
which divides
*
, and also
*
is the component of
*
i m sorry divides
*
. Climate there room
*
and also
*
together that

*
*
*

(6)
*
*
*

(7)

Solving

*
for
*
gives


(8)

It then adheres to that

*
*
*

(9)
(10)
(11)

It as such follows the

*
is never prime! In fact, the much more general result that


(12)

is never prime for

*
an essence
*
=0" /> likewise holds (Honsberger 1991).


SEE ALSO: Amenable Number, Composite Number Problem, Grimm"s Conjecture, very Composite Number, prime Factorization prime Gaps, element Number, Weakly Prime
REFERENCES:

Honsberger, R. Much more Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp.19-20, 1991.

Sloane, N.J.A. Sequence A002808/M3272in "The On-Line Encyclopedia of integer Sequences."


Referenced ~ above benidormclubdeportivo.org|Alpha: Composite Number
CITE THIS AS:

Weisstein, Eric W. "Composite Number."From benidormclubdeportivo.org--A benidormclubdeportivo.org web Resource. Https://benidormclubdeportivo.org/CompositeNumber.html


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